Seorang penjual beras mencampur 3 jenis beras. campuran pertama terdiri atas 1 kg jenis a , 2 kg jenis b , dan 4 kg jenis c dijual dengan harga rp.19.500 . campuran beras kedua terdiri dari 2 kg jenis a dan 3 kg jenis b dijual harga rp.19.000 . campuran beras ketiga terdiri atas 1 kg jenis b dan 1 kg jenis c dijual dengan harg rp.6.250 . harga beras jenis manakah yang paling mahal

Translation to English:

A rice supplier mixes three different types of rice into three different blends; Type A, Type B, and Type C.

He blends 1 kg of type A, 2 kg of type B, and 4 kg of type C and sells the blend for IDR 19500
He also blends 2 kg of type A and 3 kg of type B and sells the blend for IDR 19000
The third blend consists of 1 kg of type B and 1 kg of type C and this blend is sold for IDR 6250

Which type of rice is the most expensive?

Solution:

Start with the third blend:
1 kg of type B + 1 kg of type C = 6250
B + C = 6250
B = 6250 - C

Then move on to the second blend:
2 kg of type A + 3 kg of type B = 19000
2A + 3B = 19000
2A + 3(6250 - C) = 19000
2A + 18750 - 3C = 19000
2A - 3C = 19000 - 18750
2A - 3C = 250
2A = 250 + 3C
A = [250 + 3C] / 2

Then move on to the first blend:
1 kg of type A + 2 kg of type B + 4 kg of type C = 19500
A + 2B + 4C = 19500
 ⇒ Multiply each term by 2







B + C = 6250
B + 1964.3 = 6250
B = 6250 - 1964.3
B = 4285.7

A = [250+C] /2
A = [250 + 1964.3] / 2
A = 1107.15

The most expensive rice is type B